# How do you evaluate |9+ - 12+ 5+ - 8|?

Mar 26, 2017

$| 9 + \left(- 12\right) + 5 + \left(- 8\right) | = 6$

#### Explanation:

First evaluate whatever is inside the absolute value symbols.

As far as PEMDAS, there is only addition and subtraction, so just move from left to right.

$| \textcolor{red}{9 + \left(- 12\right)} + 5 + \left(- 8\right) | \textcolor{w h i t e}{\text{XXX}}$ Add the first two terms together.
$| \textcolor{red}{\left(- 3\right)} + 5 + \left(- 8\right) |$
$| \textcolor{\mathmr{and} a n \ge}{\left(- 3\right) + 5} + \left(- 8\right) | \textcolor{w h i t e}{\text{XXXX}}$ Now add that number to the next term.
$| \textcolor{\mathmr{and} a n \ge}{2} + \left(- 8\right) |$
$| \textcolor{\lim e g r e e n}{2 + \left(- 8\right)} | \textcolor{w h i t e}{\text{XXXXXXXXX}}$ Now add that number to the next term.
$| \textcolor{\lim e g r e e n}{- 6} |$

$\textcolor{b l u e}{| - 6 |} \textcolor{w h i t e}{\text{XXXXXXXXX}}$ Finally, take the absolute value of this number.

The absolute value of a number is just its distance (how far away it is) from $0$.

Even though $\textcolor{b l u e}{- 6}$ is negative, distance cannot be negative, so we say that $\textcolor{b l u e}{- 6}$ is a distance of $6$ away from $0$.

In other words,
$\textcolor{b l u e}{| - 6 |} = 6$

So the final answer is $6$.

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(Remember, absolute value is never negative, since it is the distance from zero. Absolute value of a positive number is just that number, and absolute value of a negative number is that number with a positive sign instead of a negative sign.)